Optical testing of a semiconductor

ABSTRACT

A method of optically testing electrical parameters of a surface of a semiconductor including carrier mobility and recombination time is disclosed which includes the step of irradiating the surface with a first beam of monochromatic light having a wavelength less than the wavelength corresponding to the band-gap energy of the semiconductor, resulting in the excitation of electrons and holes at the semiconductor surface. The surface is simultaneously irradiated with a second beam of monochromatic light having a wavelength larger than the wavelength corresponding to the band-gap energy of the semiconductor, whereby part of the second beam is reflected from the surface. The intensity of this reflected beam is measured and the magnitude thereof is a measure of the carrier mobility and recombination time at the semiconductor surface.

This invention relates to a method of optically testing electricalparameters of a semiconductor surface including carrier mobility andrecombination time.

The fabrication of integrated circuit (IC) devices involves manysophisticated processing steps such as polishing, etching, oxidation,masking, diffusion, metallization and bonding. However, in general, itis very difficult, expensive and time consuming to spot check, test andmonitor all of these processes on the production line. Electricaltesting cannot be done before the metallization has been made. Normallythis is too late for correcting any preceding process which may havegone wrong, and it may be impossible then under factory conditions tofind out which process step was at fault.

The yield in IC manufacturing could be improved significantly if one hada method for testing silicon wafers in room-temperature air between thevarious processing steps without the need for touching the wafers. Whatone needs to measure is not necessarily the electrical functioning ofthe circuit, but only one or two electrical parameters which aresensitive to variations of the process and particularly to the qualityof the silicon surface and/or the silicon-silicon dioxide interface. Thepresent invention provides an optical technique used to give a measurefor the carrier mobility and the recombination time near the siliconsurface.

In the drawings:

FIG. 1 is a cross-sectional view illustrating diagrammatically the useof two different laser beams in the present novel method.

FIG. 2 is a cross-sectional view illustrating diagrammatically anotherembodiment of the present novel method whereby one of the laser beams issplit into two coherent beams.

FIG. 3 is a cross-sectional view illustrating diagrammatically a thirdembodiment of the present novel method.

The present novel invention utilizes the influence of free electrons andholes on the refractive index of a semiconductor material. Therefractive index for a material is the ratio of the sine of the angle ofincidence to the sine of the angle of refraction when a light raypassing through a vacuum (or for practical purposes air) strikes thesurface of the material and is divided into a reflected ray and arefracted ray. The effectiveness of the semiconductor surface inreflecting light, i.e., its reflectivity, is thus influenced by theindex of refraction for the semiconductor material and may be monitoredby measuring the intensity of the reflected ray. The main idea of thepresent method is to excite high concentrations of free carriers in thesurface layer of the semiconductor with a high-power laser of wavelengthshorter than band gap. This induced free-carrier concentration will givea small decrease in the refractive index, which can be probed bysimultaneously reflecting from the semiconductor surface a beam of along-wavelength laser. The magnitude of this change and its timedependence will be determined by the carrier recombination time, τ, andby the carrier mobility, μ. Both of these parameters are sensitive tocrystal perfection, doping and surface (or interface) condition, andwill therefore be a good indicator of the process perfection.

Referring to FIG. 1 of the drawings, there is shown a substrate 10 ofsemiconductor material which may be part of a silicon wafer. In order tooptically test various electrical parameters including carrier mobility,μ (average of the electrons and holes), and recombination time, τ, neara surface 12 of the substrate 10, I disclose a method comprisingirradiating an area of the surface 12 uniformly with a first beam 14 ofmonochromatic light, preferably a laser beam, having a wavelength λ₁less than the wavelength corresponding to the band-gap energy of thesemiconductor substrate 10. For silicon having a band-gap energy of1.106 eV (electronvolt), the corresponding wavelength is 1.12micrometers. If λ₁ is less than about 1 micrometer, substantially all ofthe light beam 14 energy is absorbed in a very thin layer adjacent thesurface 12, resulting in the excitation of electrons and holes near thesurface 12. This excitation could be done in principle with anultraviolet nitrogen laser. However, the convenience of visible lightfor focusing purposes makes the use of a pulsed dye laser 16 (λ₁ =0.5micrometers), pumped by nitrogen, preferable for the first light beam14. Under these conditions, the steady-state concentration, p, of freecarriers is: ##EQU1## where N_(L) is the laser power, A is the spot areaof the irradiated surface 12 which must have a diameter larger than L,and L is the carrier diffusion length equal to √Dτ where D is thecarrier diffusion constant. The number on the right-hand side iscalculated for A=0.25 mm², λ₁ =0.5μ, τ=10⁻⁶ seconds and L=30μ, if N_(L)is written in watts. Values for p at different power levels, N_(L), arelisted at column two in Table I.

                                      TABLE I                                     __________________________________________________________________________                                   REFLECT-                                            INDUCED           UNIFORM VITY    UNIFORM GRATING GRATING                     FREE              EXCITATION                                                                            AT      EXCITATION                                                                            EXCITATION                                                                            EXCITATION             LASER                                                                              CARRIER           NORMAL  BREWSTER'S                                                                            BREWSTER'S                                                                            NORMAL  BREWSTER'S             POWER                                                                              CONCENTRATION     REFLECTION                                                                            ANGLE   REFLECTION                                                                            REFLECTION                                                                            REFLECTION             N.sub.L                                                                            p[cm.sup.-3 ]                                                                             Δ                                                                             Δ.sub.1                                                                         R.sub.B Δ.sub.2                                                                         Δ.sub.3                                                                         Δ.sub.4          __________________________________________________________________________    100 mW                                                                             3.4 × 10.sup.16                                                                     1.0 × 10.sup.-4                                                               1.3 × 10.sup.-4                                                                 2.1 × 10.sup.-9                                                                 1.3 × 10.sup.-4                                                                 7.1 × 10.sup.-8                                                                 2.2 ×                                                                   10.sup.-3              1  W 3.4 × 10.sup.17                                                                     1.0 × 10.sup.-3                                                               1.3 × 10.sup.-3                                                                 2.1 × 10.sup.-7                                                                 1.3 × 10.sup.-2                                                                 7.1 × 10.sup.-6                                                                 2.2 ×                                                                   10.sup.-1              10  W                                                                              3.4 × 10.sup.18                                                                     1.0 × 10.sup.-2                                                               1.3 × 10.sup.-2                                                                 2.1 × 10.sup. -5                                                                1.3     7.1 × 10.sup.-4                                                                 2.2 ×                                                                   10.sup.1               100  W                                                                             3.4 × 10.sup.19                                                                     1.0 × 10.sup.-1                                                               1.3 × 10.sup.-1                                                                 2.1 × 10.sup.-3                                                                 1.3 × 10.sup.2                                                                  7.1 × 10.sup.-2                                                                 2.2 ×                                                                   10.sup.3               1 RW 3.4 × 10.sup.20                                                                     1.0   1.3     2.1 × 10.sup.-1                                                                 1.3 × 10.sup.4                                                                  7.1     2.2 ×                                                                   10.sup.5               __________________________________________________________________________

In order to avoid heating of the substrate 10, the first laser beam 14should be pulsed such that the average power stays below about N≃10milliwatts. With a practical pulse repetition frequency, 1/t_(r), of 10cycles per second, this gives a pulse duration time of t_(p) =t_(r)N/N_(L) ≃100 μsec.

The surface 12 of the substrate 10 is simultaneously irradiated with asecond beam 18 of monochromatic light, preferably a second laser beam,having a wavelength λ₂ larger than the wavelength corresponding to theband-gap energy of silicon, whereby part of the second beam 18, shown asreflected beam 20, is reflected from the surface 12. As furtherexplained below, the speed requirement for detecting the reflected beam20 sets a limit for λ₂, since a fast semiconductor detector is utilized.Consequently, I use for the second laser beam 18 an infrared He-Ne laser22 having a wavelength λ₂ equal to 3.39 micrometers.

The intensity of the reflected beam 20 is now measured by utilizing aphotodetector. In the present embodiment, an InSb junction detector 24is placed at an angular position to receive the reflected beam 20, asillustrated in FIG. 1. The InSb junction detector is a relatively fastsemiconductor detector, which has a cut-off wavelength of 5.4micrometers in liquid nitrogen and a cut-off of 5.0 micrometers inliquid helium. With a pulse duration time of about 100 μsec, theresponse time of the detector 24 has to be at least 100 μsec. Theintensity of the reflected beam 20 is a measure of the carrier mobilityand recombination time at the semiconductor surface 12 since the indexof refraction, and through that, the reflectivity are affected by theinduced free-carrier concentration. The magnitude of this change will bedetermined by the carrier recombination time, τ, and by the carriermobility, μ, at the semiconductor surface. Both of these parameters aresensitive to conditions existing at semiconductor surface 12 includingcrystal perfection and doping level, and will therefore be goodindicators of the process perfection.

When the second laser beam 18 strikes the surface 12 uniformly at anangle perpendicular to the plane of the surface 12, as shown in FIG. 3,the surface reflectivity, i.e., the effectiveness of the surface 12 inreflecting the beam 18, may be mathematically expressed as follows:##EQU2## where c is the speed of light, n is the refractive index of thesemiconductor lattice, and m is the carrier effective mass. The relativechange of R.sub.⊥ due to free carriers, which is thesignal-to-background ratio, Δ₁ is: ##EQU3## Table I provides values forΔ and Δ₁ at different power levels for the first laser beam 14. Thevalues for Δ₁ as listed in Table I indicate that the effect ismeasurable, but it requires a rather high-power laser.

Better results may be achieved if the second laser beam 18 is polarizedparallel to the plane of incidence, by means of a polarizer 34 as shownin FIG. 1, and strikes the surface 12 uniformly at an angle of incidenceΘ_(I) equal to Brewster's angle defined by the relationship TAN Θ₁ =n,where n is the refractive index of the semiconductor substrate 10. Ifthe laser beam 18 is polarized parallel to the plane of incidence, thereflection without induced free carriers can in theory be reduced tozero for the Brewster's angle of incidence, Θ_(B) =73.6 degrees. Thereflectivity at Brewster's angle for a change in refractive index byfree carriers, where n=3.4 is: ##EQU4## More important than R_(B) is itsratio to the background, i.e., to the residual reflection (in theabsence of free carriers) due to incomplete polarization and to thedivergence of the laser beam 18. This signal-to-background ratio islisted in Table I as Δ₂ =R_(B) /R_(p) +R.sub.γ, where R_(p) is thebackground reflection due to incomplete polarization and R.sub.γ is theother contribution to the background reflection from the divergence ofthe laser beam 18. The comparison with δR/R for normal incidence, Δ₁,shows the advantage of the Brewster's angle method.

In order to further discriminate against the high background reflection,one may utilize spatially periodic excitation of the free carriers. Thefirst laser beam 14, prior to irradiating the surface 12, is split intotwo coherent beams 26 and 28 which are then reunited on the surface 12at symmetrical angles of incidence β and -β, respectively, asillustrated in FIG. 2. At the area on the surface 12 where the beams 26and 28 are reunited, electrons and holes are periodically excited by anoptical interference pattern with an intensity which varies sinusoidallyalong the surface 12. The periodicity d is equal to λ₁ /2sinβ. Theresulting free-carrier concentration then becomes: ##EQU5## where q=2π/dWith λ=0.5 μm and d=L=30 μm, the angle β will be about 0.5 degrees,which should be relatively easy to control. In the present embodiment,the first beam 14 is reflected by a mirror 30 into a modified Kostersprism 32, as illustrated in FIG. 2. The modified Kosters prism 32,having coatings designed for approximately equal reflection andtransmission, splits the beam 14 into the two coherent beams 26 and 28,which are then reunited at the surface 12. The excited surface 12presents to the second laser beam 18 a reflection amplitude grating.Assuming that the spots of the two laser beams 14 and 18 on the surface12 are of equal size and in perfect registration, by utilizing theFraunhofer diffraction integral to calculate the diffraction pattern,one may obtain the signal-to-background ratio Δ₃ equal to I(φ)/I_(o),where φ is the phase angle. For the first order maxima at φ=2π, oneobtains: ##EQU6## where N is the number of grating lines equal to √A/d.For d≦L=30 μm and the area of the spot equal to 0.25 mm², then

    Δ.sub.3 =4.23 Δ.sub.1.sup.2,

which is listed in Table I. The quantity Δ₃ has to be compared with Δ₁which is the signal-to-background ratio for normal reflection withoutany diffraction grating. One may conclude from Table I that the gratinggives an advantage in signal-to-background ratio for N_(L) >100 W only.

The relatively poor signal-to-background ratio of the grating techniquecan be improved considerably if Brewster's angle reflection is used.Inserting the above expression for R_(B) into the Fraunhofer integral,one obtains: ##EQU7## For d≦L=30 μm and the spot area equal to 0.25 mm²,then

    Δ.sub.4 =16.9 μ.sub.2

which is listed in Table I. One may see that a significant improvementis obtained over the no-grating Brewster's angle case for all excitationlevels.

The dependence of the signal I(Δ₁) on the grating periodicity may beused to get a more direct measurement of L, the carrier diffusionlength. I(Δ₁) depends upon the angle β of FIG. 2 as follows: ##EQU8## Byvarying the angle β and thereby the periodicity of the opticalinterference pattern, the change in the interference of the reflectedbeam 20 due to this periodicity change may be used to determine thecarrier diffusion length in accordance with the above expression.

The present method further comprises the step of measuring the timeresponse of the reflected beam 20 by measuring the intensity decaythereof after the termination of a square pulse of the first laser beam14. The decay of the free carriers after termination of a square pulse,measured by the time decay of the reflected beam 20 intensity, is ameasure of the carrier recombination time, τ, according to the followingexpression: ##EQU9## This is a slightly faster decay than exp(-t/τ). Inorder to be able to see this decay, the detector 24 must have aresolution better than τ, which is assumed to be about 1 μsec.

The present optical testing method for semiconductors is applicable totesting and monitoring silicon wafers between the various productionsteps of IC manufacturing, and it should help to increase the factoryyield significantly. In summary, I have assumed an excitation wavelengthλ₁ =0.5 μm from a pulsed dye laser, a probing wavelength λ₂ =3.39 μmfrom an He-Ne laser, and a spot diameter of 0.5 mm. The results dependon the power of the exciting laser, N_(L), and are listed in Table I interms of signal-to-background ratios Δ₁, Δ₂, Δ₃, Δ₄ for four variations:(1) uniform excitation and normal reflection, (2) uniform excitation andBrewster's angle reflection, (3) grating-like excitation and normalreflection, and finally (4) grating-like excitation and Brewster's anglereflection. While method (1) requires very high excitation power, itnevertheless appears to be feasible with a pulsed dye laser and a cooledInSb junction detector. Method (2) gives a great improvement over (1)requiring only 10 watts of excitation power. Methods (3) and (4) requireless power than Method (1), but involve the added complexity of thegrating-like excitation. Changing the grating periodicity by changingthe angle between the interfering laser beams allows a more directdetermination of the diffusion length. The best signal-to-backgroundratio can be obtained by method (4) where less than 10 watts should besufficient for a good signal. Since visible and infrared light is usedfor excitation and probing, the present technique is applicable for baresemiconductor surfaces as well as surfaces covered with silicon dioxideor other transparent insulating layers. Focusing of the two laser beams14 and 18 into a small spot allows one to probe and scan small areas ofthe whole wafer. The present optical technique should provide, rapidlyand without touching, significantly improved control over waferuniformity and perfection between the various wafer fabrication steps.

What is claimed is:
 1. A method of optically testing electricalparameters of a surface of a semiconductor including carrier mobilityand recombination time comprising the steps of:irradiating said surfacewith a first beam of monochromatic light having a wavelength less thanthe wavelength corresponding to the band-gap energy of saidsemiconductor, whereby the energy of said light beam is substantiallyabsorbed by said surface resulting in the excitation of electrons andholes at said surface, simultaneously irradiating said surface with asecond beam of monochromatic light having a wavelength larger than thewavelength corresponding to the band-gap energy of said semiconductor,whereby part of said second beam is reflected from said surface,measuring the intensity of said reflected beam, whereby the magnitudethereof is a measure of the carrier mobility and recombination time atsaid semiconductor surface.
 2. A method as recited in claim 1 whereinthe step of irradiating said surface with said first beam is performedby pulsing said first beam in a manner such that the average power staysbelow about 10 milliwatts.
 3. A method as recited in claim 2 furthercomprising the step of measuring the time response of said reflectedbeam by measuring the intensity decay thereof after the termination of asquare pulse of said first beam, whereby the time decay of saidintensity measurement is a measure of the carrier recombination time. 4.A method as recited in claim 3 wherein said second beam of monochromaticlight irradiates said surface uniformly at an angle perpendicular to theplane of said surface.
 5. A method as recited in claim 4 furthercomprising the step wherein said first beam, prior to irradiating saidsurface, is split into two coherent beams which are then reunited onsaid surface at symmetrical angles of incidence β and -β, respectively,whereby said electrons and holes at said surface are periodicallyexcited by an optical interference pattern which varies sinusoidallyalong said surface.
 6. A method as recited in claim 5 wherein theperiodicity of said optical interference pattern is varied by varyingthe angle β, whereby the change in the intensity of said reflected beamis a measure of the carrier diffusion length in said semiconductor.
 7. Amethod as recited in claim 3 wherein said second beam of monochromaticlight is polarized parallel to the plane of incidence and strikes saidsurface uniformly at an angle of incidence Θ₁ equal to Brewster's angle,defined by the relationship TAN Θ_(I) =n, where n is the refractiveindex of said semiconductor.
 8. A method as recited in claim 7 furthercomprising the step wherein said first beam, prior to irradiating saidfirst surface, is split into two coherent beams which are then reunitedon said surface at symmetrical angles of incidence β and -β,respectively, whereby said electrons and holes at said surface areperiodically excited by an optical interference pattern which variessinusoidally along said surface.
 9. A method as recited in claim 2wherein said semiconductor is silicon, said first beam is a pulsed dyelaser beam having a wavelength of about 0.5 micrometers, and said secondbeam is an infrared He-Ne laser beam having a wavelength of about 3.39micrometers.
 10. A method as recited in claim 2 wherein said measuringstep is performed by utilizing an InSb junction detector placed at anangular position to receive said reflected beam.